Measurement of the total cross section and ρ -parameter from elastic scattering in pp collisions at √s=13 TeV with the ATLAS detector

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jats:titleAbstract</jats:title>jats:pIn a special run of the LHC with jats:inline-formulajats:alternativesjats:tex-math$$\beta ^{\star } = 2.5$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:msup mml:miβ</mml:mi> mml:mo⋆</mml:mo> </mml:msup> mml:mo=</mml:mo> mml:mn2.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> km, proton–proton elastic-scattering events were recorded at jats:inline-formulajats:alternativesjats:tex-math$$\sqrt{s} = 13$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:msqrt mml:mis</mml:mi> </mml:msqrt> mml:mo=</mml:mo> mml:mn13</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> TeV with an integrated luminosity of jats:inline-formulajats:alternativesjats:tex-math$$340~\upmu {\text {b}}^{-1}$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mn340</mml:mn> <mml:mspace /> mml:miμ</mml:mi> mml:msup mml:mrow mml:mtextb</mml:mtext> </mml:mrow> mml:mrow mml:mo-</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam jats:italict</jats:italic> variable in the range from jats:inline-formulajats:alternativesjats:tex-math$$-t = 2.5 \cdot 10^{-4}$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mo-</mml:mo> mml:mit</mml:mi> mml:mo=</mml:mo> mml:mn2.5</mml:mn> mml:mo·</mml:mo> mml:msup mml:mn10</mml:mn> mml:mrow mml:mo-</mml:mo> mml:mn4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> GeVjats:inline-formulajats:alternativesjats:tex-math$$^{2}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msup <mml:mrow /> mml:mn2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> to jats:inline-formulajats:alternativesjats:tex-math$$-t = 0.46$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mo-</mml:mo> mml:mit</mml:mi> mml:mo=</mml:mo> mml:mn0.46</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> GeVjats:inline-formulajats:alternativesjats:tex-math$$^{2}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msup <mml:mrow /> mml:mn2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section jats:inline-formulajats:alternativesjats:tex-math$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miσ</mml:mi> mml:mtexttot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, parameters of the nuclear slope, and the jats:inline-formulajats:alternativesjats:tex-math$$\rho $$</jats:tex-math><mml:math xmlns:mml=""> mml:miρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit jats:inline-formulajats:alternativesjats:tex-math$$t \rightarrow 0$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mit</mml:mi> mml:mo→</mml:mo> mml:mn0</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the jats:italict</jats:italic>-dependence. The results for jats:inline-formulajats:alternativesjats:tex-math$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miσ</mml:mi> mml:mtexttot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternativesjats:tex-math$$\rho $$</jats:tex-math><mml:math xmlns:mml=""> mml:miρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> are jats:disp-formulajats:alternativesjats:tex-math$$\begin{aligned} \sigma _{\text {tot}}(pp\rightarrow X) = 104.7 \pm 1.1 ; \text{ mb },\quad \rho = 0.098 \pm 0.011 . \end{aligned}$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mtable mml:mtr mml:mtd mml:mrow mml:msub mml:miσ</mml:mi> mml:mtexttot</mml:mtext> </mml:msub> mml:mrow mml:mo(</mml:mo> mml:mip</mml:mi> mml:mip</mml:mi> mml:mo→</mml:mo> mml:miX</mml:mi> mml:mo)</mml:mo> </mml:mrow> mml:mo=</mml:mo> mml:mn104.7</mml:mn> mml:mo±</mml:mo> mml:mn1.1</mml:mn> <mml:mspace /> <mml:mspace /> mml:mtextmb</mml:mtext> <mml:mspace /> mml:mo,</mml:mo> <mml:mspace /> mml:miρ</mml:mi> mml:mo=</mml:mo> mml:mn0.098</mml:mn> mml:mo±</mml:mo> mml:mn0.011</mml:mn> mml:mo.</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math></jats:alternatives></jats:disp-formula>The uncertainty in jats:inline-formulajats:alternativesjats:tex-math$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miσ</mml:mi> mml:mtexttot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> is dominated by the luminosity measurement, and in jats:inline-formulajats:alternativesjats:tex-math$$\rho $$</jats:tex-math><mml:math xmlns:mml=""> mml:miρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.</jats:p>


Acknowledgements: We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We are indebted to the beam optics development team, led by H. Burkhardt, for the design, commissioning and thorough operation of the high-β* optics in dedicated LHC fills. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZS, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TENMAK, Turkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020 and Marie Sklodowska-Curie Actions, European Union; Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Goran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [61].

5106 Nuclear and Plasma Physics, 5107 Particle and High Energy Physics, 5110 Synchrotrons and Accelerators, 51 Physical Sciences
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